Your inner dancer is calling. Its voice, sweet but tough and insistent, pulses in every molecule of the new Broadway musical “Billy Elliot,” demanding that you wake up sleeping fantasies of slipping on tap or ballet shoes and soaring across a stage. Few people may have the gift of this show’s title character, a coal miner’s son in northern England who discovers he was born to pirouette. But the seductive, smashingly realized premise of “Billy Elliot,” which opened Thursday night at the Imperial Theater, is that everybody has the urge. And in exploring that urge among the population of a down-at-heels coal town suffering through the British miners’ strike of the mid-1980s, this show both artfully anatomizes and brazenly exploits the most fundamental and enduring appeal of musicals themselves.

It’s been more than three years since “Billy Elliot,” directed by Stephen Daldry and featuring a score by Elton John, first sent critics and audiences into a mass swoon in London, where it continues to play. The delay in bringing the show to Broadway hinted at fears that it might not sit comfortably on American soil.

Adapted by Lee Hall from his screenplay for the affectionately remembered 2000 movie of the same title (also directed by Mr. Daldry), “Billy Elliot” is told in thick working-class accents and an argot that, even in London, necessitated putting a glossary in the program. What’s more, the show traffics in a particularly British brand of bitter treacle, wallowing in the glory of the bravely defeated and the pathos of small, trapped lives.

But the timing of the production’s arrival here, with the United States newly chastened by severe financial woes and fears, gives it a resonance it might not have had in 2005, when big spenders ruled with complacency. “Billy Elliot” is a hard-times musical. And as the culture of the Great Depression made clear, in times of economic darkness there can be blessed relief in dreams of tripping the light.

Much of the power of “Billy Elliot” as an honest tear-jerker lies in its ability to give equal weight to the sweet dreams of terpsichorean flight and the sourness of a dream-denying reality, with the two elements locked in a vital and unending dialogue. This isn’t wholesale escapism à la Busby Berkeley or “Mamma Mia!” In tone, it’s closer to the song-dotted working-class films of Terence Davies or, on television, Dennis Potter’s “Pennies From Heaven.”

This production never lets us forget the elemental tug of war between Billy’s longing to dance and the forces pulling him away from it. Mr. Daldry and his prodigiously inventive team make sure that the conflict is carried through on every level, from Peter Darling’s inspired scene-melding choreography, which gives a new spin to the idea of the integrated musical, to Ian MacNeil’s fluidly moving sets and Rick Fisher’s shadow-casting lighting. And it’s telling that Mr. John’s songs (with lyrics by Mr. Hall) are as infused with the energy of anger as of joy.

The plot, which sticks close to that of Mr. Hall’s screenplay, doesn’t even try to avoid the clichés common to tales of talented, odds-beating backwater youth. Billy is, natch, a motherless boy with a loving but unlettered father (a touching Gregory Jbara) and an adorably addled grandmother, played by the estimable Carole Shelley. Billy is portrayed by three young teenagers, Trent Kowalik, Kiril Kulish and, in the performance I saw, the excellent David Alvarez. (No public schedule is available for which Billy performs on which night.)

There’s the inevitable inspirational teacher, a Mrs. Wilkinson (the sublime Haydn Gwynne, who created the role in London), who sees a spark of greatness in the lad. There’s the time-honored progression from resistance  here by a rough, masculine culture  suspicious of all things arty (embodied by Billy’s brother, played by Santino Fontana, and his father) to acceptance, when the whole town bands together to help send the boy to London for his big audition. There are even, heaven help us, visitations by the fond ghost of Billy’s mother (Leah Hocking).

Yet Mr. Daldry and company turn tripe into triumph by making us understand the depth of the appeal of its classic show-business fairy tale, not only to us but also to the people whose dreary daily existences touch on Billy’s. The evidence of this appeal is abundant in “Billy Elliot,” most obviously in the motley ballet classes presided over by the wryly disparaging Mrs. Wilkinson and a Christmas frolic at the miners’ hall where everybody dresses up as their favorite villainess, Margaret Thatcher. But it’s not just the amateur performers who feel the ineffable pull of song and dance.

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David Alvarez, center, plays Billy Elliot in this musical adaptation of the 2000 film.Credit...Sara Krulwich/The New York Times

Billy’s grandma shucks her shabby housecoat to reveal a sparkling dress and summons a spectral chorus of partners past as she recalls the respite from an unhappy marriage provided by nights of dancing with her alcoholic husband. Mrs. Wilkinson’s grubby rehearsal pianist (Thommie Retter) strips out of his civvies to become a gyrating disco boy for a number called “Born to Boogie.”

And Billy’s best friend, Michael (Frank Dolce, who alternates with David Bologna), reveals the thrill of dressing up in his sister’s clothes and making like Sophie Tucker in the show-stopping “Expressing Yourself.” (The everyday metamorphosis-ready costumes are by Nicky Gillibrand.)

That number  and an electric outcry of frustration called “Angry Dance”  come closest to what one might expect from a venerable pop-chart topper like Mr. John. But much of his work here, far more restrained than his more mawkish scores for Disney musicals, is in a folksier vein, drawn from North country ballads and protest songs. And undercurrents of anxiety, wistfulness and melancholy run through the most tuneful pieces.

This show makes sure that we always keep in mind the grittiness and despair of the society that produced Billy, so that the poetry of his dancing seems all the more startling and inexplicable. Mr. Darling’s surreal blending of Mrs. Wilkinson’s dance class with a clash between miners and police is one of the freshest, most exciting uses of narrative dance I’ve seen in years. And until the finale (which is a tad overdone), he rations his big, knock-’em-dead sequences. “Billy Elliot,” you see, isn’t a dance show; it’s about why people need dance.

The performances, for the most part, are broader than they were in London, with more mugging and heart-tugging stickiness. But the two most essential portrayals  that of Ms. Gwynne and Mr. Alvarez  were spot-on the night I saw the show. Hard-shelled and all too wary of the limits of her life, Ms. Gwynne’s Mrs. Wilkinson perfectly embodies the tricky balance of sweet and salty the show requires.

And Mr. Alvarez, a natural lyrical dancer, exudes just the right air of conviction and perplexity. This Billy can’t articulate his need for dance, but he understands the potency and worth of his emotions. You always feel his ambivalence and, in the final scenes, his confounded sense of the privilege  and guilt  in entering another realm.

For everyone else in the play, like most of us in the audience, the transcendence of dance is something to be sampled, falteringly and only occasionally, rather than lived. Billy’s grandmother sings of her youthful nights on the dance floor: “It was bliss for an hour or so/But then they called time to go/And in the morning we were sober.”

“Billy Elliot” never doubts that it’s the sobriety that endures in life. Which makes those intoxicating, fleet-footed flashes of art, where leaden bodies fly and discord turns into harmony, all the more to be cherished.